Express this product in scientific notation: $(5.00\times 10^{-1})\times (8.00\times 10^{4})$
Answer: Start by collecting like terms together. $= (5.00\times 8.00) \times (10^{-1}\times 10^{4})$ When multiplying exponents with the same base, add the powers together. $= 40.0 \times 10^{-1\,+\,4}$ $= 40.0 \times 10^{3}$ To write the answer correctly in scientific notation, the first number needs to be between $1$ and $10$ . In this case, we need to move the decimal one position to the left without changing the value of our answer. $ $ We can use the fact that $40.0$ is the same as $4.000 \times 10$ $ = {4.000 \times 10} \times 10^{3} $ $= 4.000\times 10^{4}$